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Title: Linguistic probability theory
Author: Halliwell, J. L.
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2008
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A theory of linguistic probabilities as is patterned after the standard Kolmogorov axioms of probability theory. Since fuzzy numbers lack algebraic inverses, the resulting theory is weaker than, but generalizes its classical counterpart. Nevertheless, it is demonstrated that analogues for classical probabilistic concepts such as conditional probability and random variables can be constructed. In the classical theory, representation theorems mean that most of the time the distinction between mass/density distributions and probability measures can be ignored. Similar results are proven for linguistic probabilities. From these results it is shown that directed acyclic graphs annotated with linguistic probabilities (under certain identified conditions) represent systems of linguistic random variables. It is then demonstrated these linguistic Bayesian networks can utilize adapted best-of-breed Bayesian network algorithms (junction tree based inference and Bayes’ ball irrelevancy calculation). These algorithms are implemented in Arbor, an interactive design, editing and querying tool for linguistic Bayesian networks. To explore the applications of these techniques, a realistic example drawn from the domain of forensic statistics is developed. In this domain the knowledge engineering problems cited above are especially pronounced and expert estimates are commonplace. Moreover, robust conclusions are of unusually critical importance. An analysis of the resulting linguistic Bayesian network for assessing evidential support in glass-transfer scenarios highlights the potential utility of the approach.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available